Journal d’Analyse Mathématique

, Volume 75, Issue 1, pp 67–84

# On global integrability of BMO functions on general domains

Article

## Abstract

Extending results of Staples and Smith-Stegenga, we characterize measurable subsets of a given domainDR n on which BMO(D) functions areL p integrable or exponentially integrable. In particular, we characterize uniform domains by the integrability of BMO functions. We also remark on the boundedness of domains satisfying a certain integrability condition for the quasihyperbolic metric.

## Keywords

Constant Factor Unbounded Domain General Domain Measurable Subset Global Integrability
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## References

1. [1]
F. W. Gehring and B. G. Osgood,Uniform domains and the quasihyperbolic metric, J. Analyse Math.36 (1979), 50–74.
2. [2]
Y. Gotoh,BMO extension theorem for relative uniform domains, J. Math. Kyoto Univ.33 (1993), 171–193.
3. [3]
Y. Gotoh,On decomposition theorem for BMO and VMO, to appear.Google Scholar
4. [4]
J. John and L. Nirenberg,On the functions of bounded mean oscillation, Comm. Pure Appl. Math.14 (1961), 415–426.
5. [5]
P. Jones,Extension theorems for BMO, Indiana Univ. Math. J.29 (1980), 41–66.
6. [6]
H. M. Reimann,Functions of bounded mean oscillation and quasiconformal mappings, Comment. Math. Helv.49 (1974), 260–276.
7. [7]
H. M. Reimann and T. Rychener,Funktionen beschränkter mittelerer Oszillation, Lecture Notes in Math.489, Springer, Berlin, 1975.Google Scholar
8. [8]
W. Smith and D. Stegenga,Exponential integrability of the quasihyperbolic metric on Hölder domains, Ann. Acad. Sci. Fenn. Ser. A I Math.16 (1991), 345–360.
9. [9]
S. G. Staples,L p-averaging domains and the Poincaré inequality, Ann. Acad. Sci. Fenn. Ser. A I Math.14 (1989), 103–127.
10. [10]
E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.Google Scholar